*4.3. Identification of the Maximum Power Capacity of the ESS in the Considered Node of the VPP Regarding the Power Quality Voltage Profile*

In terms of VPP efficiency and sensitivity, it is important to identify the maximum level of ESS power capacity that can be connected to the planned node. In order to identify the maximum power capacity of the ESS, it is proposed to conduct investigations with power quality parameters of the grid and requirements for the integration of the generation units with power systems. The impact of ESS power capacity on economic efficiency is considered in paper [36]. In this paper, the maximum power capacity of *ESS-L* is identified using a simplified analytic derivation, as well as Matlab modeling and simulation.

A rough estimation of the maximum power capacity of the considered battery energy storage *ESS-L* connected to the same node of MV network as hydro power plant *HPP-*L can be calculated based on short circuit power related to the connection point of *ESS-L* and *HPP-L*. The simplified one-phase Thevenin's equivalent circuit, which can be used for rough calculations, is presented in Figure 11.

**Figure 11.** Simplified one-phase Thevenin's equivalent circuit used for a rough estimation of the influence of power capacity of considered hydro power plant and energy storage system on voltage level.

In a simplified estimation of the influence of the selected generation unit on the voltage condition in the connection point, a critical simplification can be considered. Firstly, the investigated network is treated as unloaded so that the decrease of voltage caused by the load is not taken into consideration. Only the direct influence of the considered generation is then revealed. As a result of the mentioned assumption, before the connection of the power unit, the Thevenin's substitute voltage source magnitude *ET* in the point of common coupling (PCC) is the equal nominal voltage. The Thevenin's reactance *XT* is equal to short circuits reactance *XQ* addressed to the node of the connection point. The resistance of Thevenin's equivalent can be neglected in comparison to reactance. The parameters of Thevenin's equivalent circuits can be calculated as:

$$E\_T = \frac{\mathcal{U}\_N}{\sqrt{3}}\tag{2}$$

$$X\_T = X\_Q = \frac{c \cdot U\_N^2}{S\_{kQ}},\tag{3}$$

where:


Due to the high influence of reactive power on the voltage level, the second critical assumption in the simplified calculation is that the *HPP-L* and *ESS-L* only generate a reactive power in the PCC. The voltage change is caused by a voltage associated with the short circuit reactance and current flow *IPCC* inserted into the network by both generating units connected to the PCC operating at maximum power. The estimated steady state voltage change visible in the PCC can be expressed by:

$$
\Delta l l\_{\text{C}} = \sqrt{3} \cdot I\_{\text{PCC}} \cdot X\_{Q} = \sqrt{3} \cdot \frac{S\_{\text{PCC}}}{\sqrt{3} \cdot l I\_{N}} \cdot \frac{c \cdot l l\_{N}^{2}}{S\_{kQ}} = c \cdot l l\_{N} \cdot \frac{S\_{\text{PCC}}}{S\_{kQ}} \tag{4}
$$

where: *SPCC*—the maximum power capacity of the power generation unit connected to the PCC, which in the described case study is a sum of generated power HPP and ESS—*SPCC* = *SHHP* + *SESS*.

Combining definition of voltage change *dC* introduced in Equation (1) with Equation (4) allows deriving a direct relation between maximum power capacity of considered power generation unit connected to the PCC (*SPCC*) with the short circuit power which characterizes equivalent of the network visible in point of the PCC (*SkQ*). This relation can be revealed as:

$$d\_{\mathbb{C}} = \frac{|\Lambda \mathcal{U}\_{\mathbb{C}}|}{\mathcal{U}\_{N}} = c \cdot \frac{\mathcal{S}\_{\text{PCC}}}{\mathcal{S}\_{kQ}}.\tag{5}$$

Equation (5) can be recalculated in order to express the maximum power capacity of the power generating unit connected to the considered PCC which is characterized by short circuit power. Short circuit power depends on the permissible level of rapid voltage change.

$$S\_{\rm PCC} = \frac{d\_c}{c} \cdot S\_{kQ}.\tag{6}$$

Short circuit power in the selected node of the investigated power network, that is, in the busbar of the main station *R-J* and in the connection point of the hydropower plant *HPP-L* and battery energy storage system *ESS-L,* are presented in Table 4. Next, taking into account permitted levels of rapid voltage change *dc* = 3% and short circuit factor of *c* = 1.1 as quoted in Section 2, it is possible to use Equation (6) to estimate the maximum capacity of the power generating units that can be connected to the investigated node of the power network from the point of view of rapid voltage change requirement. An example of the calculation, in relation to the main power station *R-J* and the connection point of the hydropower plant and energy storage system (node L), is compared in Table 4. It can be concluded that the nodes located deep in the power grid are characterized by a lower level of short circuit power which ultimately increases the limitation of the capacity of the generating unit that can be connected in that node. When referring to the connection node of the hydropower plant and energy storage system, which is characterized by short circuit power on the level of 54.2 MVA, the maximum power capacity of the generation unit is limited to 1.48 MW. Assuming the operation of the hydropower plant *HPP-L* with a maximum power level of 0.94 MW, it can be concluded that the permissible power of the energy storage system *ESS-L* connected to the same node is limited to 0.54 MW. The presented calculation results of the possible power of the battery energy storage *ESS-L* should be treated as a rough estimation. The results are extremely limited by the simplification of the network, the unloaded condition, the reactive power consideration and the restricted limit of the rapid voltage change *d*c = 3%.

**Table 4.** Short circuit power in the selected node of the investigated power network and the estimated maximum power capacity of the power generation unit permissible in terms of rapid voltage change requirements.


In order to obtain a more precise estimation of the desired value of the maximum power capacity of the *ESS-L,* a simulation of the influence of gradually increasing the power of the *ESS-L* on the voltage level in the connection point of the *HPP-L* and *ESS-L* is proposed. The basic conditions of the simulation are similar to those previously used when the effect of switching on the DER series on the voltage level was simulated. These preliminary assumptions are as follows—the initial power flows relate to summer peak load demand and the *HHP-L* power generation level is a maximum of around 940 kW. The result of the simulation is presented in Figure 12. The results allow concluding that from the point of view of acceptable rapid voltage changes at the point of connection of *HPP-L* and *ESS-L*, the total maximum capacity of these two generating units should be in the range from 2 MW to 2.4 MW. Assuming that the power generated by *HPP-L* is around 1 MW, it can be concluded that the possible maximum capacity of a given energy storage system *ESS-L* is limited to 1 MW or 1.4 MW. In comparison with the method based on simplified calculations using short circuit power circuits, the result obtained using more precise simulations is more realistic.

The rough estimation using short circuit power is the fast method, however, usually gives relatively underestimated results. The short-circuit equivalent model is dedicated to the linear electrical components. In addition, the short circuit current is significantly modified in the presence of power electronic inverters used to integrate DERs and ESSs into the power supply system. The results of the calculation of the maximum power of a given ESS using network modeling are more technically realistic but require modeling and computing power. It should be mentioned that the estimation of the maximum power capacity of a considered ESS based on modeling and simulation is more accurate as it includes:


The presented results were used in the accompanying paper [36] in the point concerning the economic efficiency test where a 0.5 MW or 1 MW battery energy storage system is considered to be used in the VPP topology. In Reference [36] general aspects related to VPP concepts were also examined, including the analysis of the advantages and disadvantages of using one ESS compared to many small ESSs or more RES.

**Figure 12.** Voltage changes at the point of connection of MV *HPP-L* and *ESS-L* during the gradual increase of maximum power of power generators.
